Imho we have to distinguish between carbon markets and allowing carbon offsets. The EU emission trading scheme for example just issues a number of certificates and forces certain emitters to purchase them in an open auction. So you put a variable price on carbon and create an incentive to reduce emissions due to regular reductions of the certificates offered. The money is then used to invest into green technology or handed out to the general public. This works thanks to not having carbon offsets.
Carbon offsets do not really work, as they are often just fake and if not mostly just take land from the poor to put it under conservation. Usually that is just removing people, who treat the land well anyway, so it has not benefit for nature, but hurts poor people.